This invention relates to methods for modeling temporal processes in a body of material in computer aided design (CAD) and electronic design automation (EDA) systems. For example it may be used to model semiconductor fabrication process steps such as epitaxial growth in crystalline material structures, which are later used to fabricate integrated circuit devices.
Various methods can be used for modeling temporal processes in a body of material. Processes involving particle movement or chemical reactions often are best modeled using discrete time probability functions. The Kinetic Monte Carlo (KMC) method is a Monte Carlo computer simulation method that simulates time evolution of certain processes occurring at a known rate, modeled by such discrete time probability functions. See A. F. Voter, Introduction to the Kinetic Monte Carlo Method, in Radiation Effects in Solids, edited by K. E. Sickafus, E. A. Kotomin and B. P. Uberuaga (Springer, NATO Publishing Unit, Dordrecht, The Netherlands, 2007) pp. 1-23, incorporated by reference herein.
In a KMC method, events are modeled as having a predefined probability of occurring per unit time. For modeling a dopant diffusion process, for example, there is a known probability at which a dopant atom will jump in each direction during a particular time step. The probability increases with increasing temperature. The probability per time step, which can also be thought of as a frequency of occurrence v, is given by:
      v    =                  v        0            ·              exp        ⁡                  (                                    -                              E                a                                                                    k                B                            ⁢              T                                )                      ,where                v0 is a pre-factor that is determined by the properties of a material where the event is occurring and the properties of the particle under consideration;        Ea is an activation energy of the event, such as the energy barrier for the particle jumping from one location to the next;        kB is Boltzmann's constant, and        T is temperature        
Thus to model a process in which events occur randomly, with a frequency that depends on the values of certain properties of the particle of interest and properties of the local material, an embodiment might use discrete time probability functions at each of the nodes, with the parameters of the node function (v0, Ea and T in the above example) assigned values based on the material and conditions extant at each grid node. The time step for the simulation is typically chosen based on the time scale at which the event is likely to occur. If multiple concurrent random processes are to be modeled, then the time step for the simulation is typically chosen based on the time scale at which the most frequent event is likely to occur.
A computer simulation is a simulation, run on a single computer, or a network of computers, to reproduce behavior of a physical system. The simulation applies a model to simulate the system. Computer simulations have become a useful part of mathematical modeling of many natural systems in physics (computational physics), electronics, chemistry, and engineering. Simulation of a system is represented as the computer execution of the system's model. Computer simulation may be used to explore and gain insights into new technology and to estimate the performance or other behaviors of complex systems.
Epitaxy refers to the formation of a crystalline overlayer on a crystalline substrate. The overlayer is called an epitaxial film or epitaxial layer. For most technological applications, it is desired that the deposited material form an epitaxial layer that has one well-defined crystalline orientation with respect to the substrate crystal structure (i.e., single-domain epitaxy).
Epitaxy is used in nanotechnology, in semiconductor fabrication, and to create monolayer and multilayer films on crystalline surfaces. Epitaxy is particularly useful for compound-material semiconductors such as gallium arsenide transistors. Epitaxial silicon is often formed using vapor-phase epitaxy, a type of chemical vapor deposition. Molecular-beam and liquid-phase epitaxy are also used, for example for compound semiconductors. Solid-phase epitaxy is used is used in applications such as crystal-damage healing.
Epitaxial films may be grown from gaseous or liquid precursors. Because the substrate acts as a seed crystal, the deposited film may orient into one of a defined set of discrete orientations with respect to the substrate crystal. This is referred to as epitaxial growth. If the overlayer either forms an orientation that is not one of a defined set of discrete orientations with respect to the substrate, or does not form an ordered overlayer, it is termed non-epitaxial growth. If an epitaxial film is deposited on a substrate of the same composition, the process is called homoepitaxy; otherwise it is called heteroepitaxy.
Simulation of epitaxial growth is of critical importance for new microelectronic devices, especially for FinFETS and FinFET derived technologies (e.g., horizontal nanowires and “Gate All Around” devices), as well as new or revised semiconductor fabrication processes. Continuum models for epitaxial growth, based on finite element calculations or level-set algorithms, are not good at predicting the correct growth shapes, mostly because they tend to turn and smooth the corners, and also because epitaxial growth is very sensitive to orientation. Lattice Kinetic Monte Carlo (LKMC) models may be utilized [1, 2] but in some cases they can be slow to execute. Faster simulation using LKMC models would provide an improved solution for epitaxial growth problems.
Regular Lattice KMC simulation (i.e., mapping atoms one-to-one with the material density) is a conventional process to simulate epitaxy. In particular, Synopsys Sentaurus Process KMC and the Open Source MMonCa [4] implement conventional solutions to this same problem. Both are incorporated by reference herein.
The following background reference documents are incorporated by reference herein:                [1] I. Martin-Bragado and V. Moroz. Appl. Phys. Lett. 95, 123123 (2009)        [2] Chen et al. SISPAD, Glasgow, 2013, pp. 9-12.        [3] D. T. Gillespie, J. Comput Phys. 22 (1976) 403.        [4] I. Martin-Bragado et al. Computer Physics Communications 184 (2013) 2703-2710.        